{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T11:24:35Z","timestamp":1762514675369,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T00:00:00Z","timestamp":1762473600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A novel multiple attribute group decision-making (MAGDM) model is introduced in this study, utilizing a diversified hesitant fuzzy multi-granulation information system to address challenges in incomplete information settings. The analysis commences with an exploration of hesitant fuzzy sets and multi-granulation approximation. Subsequently, the integration of cumulative prospect theory into Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) within a hesitant fuzzy framework is discussed, emphasizing the incorporation of a risk preference coefficient in GDM to enhance individual assessments. The model proposes a systematic approach to address various MAGDM scenarios under hesitant fuzzy conditions. An illustrative case study on resource-sharing is provided to demonstrate the efficacy of the diversified MAGDM model, with evaluation outcomes expressed using hesitant fuzzy elements, offering valuable insights into group decision-making in hesitant fuzzy environments.<\/jats:p>","DOI":"10.3390\/sym17111903","type":"journal-article","created":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T10:56:45Z","timestamp":1762513005000},"page":"1903","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hesitant Fuzzy Multi-Granulation Rough Set Model Based on Similarity Assessment"],"prefix":"10.3390","volume":"17","author":[{"given":"Junxiao","family":"Ren","sequence":"first","affiliation":[{"name":"School of Humanities, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Humanities, Xidian University, Xi\u2019an 710071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/s41066-021-00253-7","article-title":"Novel score functions of generalized orthopair fuzzy membership grades with application to multiple attribute decision making","volume":"7","author":"Feng","year":"2021","journal-title":"Granul. Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2689","DOI":"10.1109\/TFUZZ.2020.3006559","article-title":"Maximum Fuzzy Consensus Feedback Mechanism With Minimum Cost and Private Interest in Group Decision-Making","volume":"29","author":"Zhang","year":"2021","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_3","first-page":"463","article-title":"On variable-precision-based rough set approach to incomplete interval-valued fuzzy information systems and its applications","volume":"40","author":"Li","year":"2021","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"6186183","DOI":"10.1155\/2024\/6186183","article-title":"Some Information Measures for Interval-Valued Hesitant Fuzzy Sets in Multiple Criteria Decision-Making","volume":"2024","author":"Chen","year":"2024","journal-title":"Int. J. Intell. 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Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"119850","DOI":"10.1016\/j.ins.2023.119850","article-title":"An optimization-based three-way decision for multi-criteria ranking strategy considering intuitionistic fuzzy concept","volume":"654","author":"Mao","year":"2024","journal-title":"Inf. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"116013","DOI":"10.1016\/j.eswa.2021.116013","article-title":"Group risk assessment in failure mode and effects analysis using a hybrid probabilistic hesitant fuzzy linguistic MCDM method","volume":"188","author":"Wang","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"106331","DOI":"10.1016\/j.cie.2020.106331","article-title":"Variable precision diversified attribute multigranulation fuzzy rough set-based multi-attribute group decision making problems","volume":"142","author":"Sun","year":"2020","journal-title":"Comput. Ind. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.ins.2022.03.048","article-title":"Multi-granularity dominance rough concept attribute reduction over hybrid information systems and its application in clinical decision-making","volume":"597","author":"Chu","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"13085","DOI":"10.1007\/s00500-019-03853-3","article-title":"Multi-granulation hesitant fuzzy rough sets and corresponding applications","volume":"23","author":"Zhang","year":"2019","journal-title":"Soft Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1016\/j.cie.2018.11.020","article-title":"A trust propagation and collaborative filtering based method for incomplete information in social network group decision making with type-2 linguistic trust","volume":"127","author":"Wu","year":"2019","journal-title":"Comput. Ind. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1780","DOI":"10.1109\/TFUZZ.2022.3214267","article-title":"A Novel Diversified Attribute Group Decision-Making Method Over Multisource Heterogeneous Fuzzy Decision Systems With Its Application to Gout Diagnosis","volume":"31","author":"Ye","year":"2023","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.ins.2021.06.088","article-title":"A three-way decision method based on fuzzy rough set models under incomplete environments","volume":"577","author":"Ye","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.fss.2018.05.017","article-title":"Fuzzy neighborhood operators and derived fuzzy coverings","volume":"370","author":"Yang","year":"2019","journal-title":"Fuzzy Sets Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"8291","DOI":"10.1007\/s00500-018-3465-6","article-title":"Fusions and preference relations based on probabilistic interval-valued hesitant fuzzy information in group decision making","volume":"23","author":"Zhang","year":"2019","journal-title":"Soft Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"103651","DOI":"10.1016\/j.engappai.2020.103651","article-title":"A novel three-way decision method in a hybrid information system with images and its application in medical diagnosis","volume":"92","author":"Li","year":"2020","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"e13357","DOI":"10.1111\/exsy.13357","article-title":"A new method of multi-attribute group decision making based on hesitant fuzzy soft expert information","volume":"40","author":"Akram","year":"2023","journal-title":"Expert Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2039","DOI":"10.1007\/s41066-023-00414-w","article-title":"Multi-criteria group decision-making based on the combination of dual hesitant fuzzy sets with soft expert sets for the prediction of a local election scenario","volume":"8","author":"Ali","year":"2023","journal-title":"Granul. Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.ins.2020.05.039","article-title":"Neighborhood rough set-based three-way clustering considering attribute correlations: An approach to classification of potential gout groups","volume":"535","author":"Chu","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.ijar.2022.08.017","article-title":"A constructing approach to multi-granularity object-induced three-way concept lattices","volume":"150","author":"Hu","year":"2022","journal-title":"Int. J. Approx. Reason."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.knosys.2018.03.013","article-title":"Deriving heterogeneous experts weights from incomplete linguistic preference relations based on uninorm consistency","volume":"150","author":"Cheng","year":"2018","journal-title":"Knowl. Based Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.inffus.2019.07.013","article-title":"Diversified binary relation-based fuzzy multigranulation rough set over two universes and application to multiple attribute group decision making","volume":"55","author":"Sun","year":"2020","journal-title":"Inf. Fusion"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1007\/s40314-020-01216-5","article-title":"Diversified multiple attribute group decision-making based on multigranulation soft fuzzy rough set and TODIM method","volume":"39","author":"Sun","year":"2020","journal-title":"Comput. Appl. Math."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/j.matcom.2023.12.021","article-title":"Distance and similarity measures of Hesitant bi-fuzzy set and its applications in renewable energy systems","volume":"219","author":"Gupta","year":"2024","journal-title":"Math. Comput. Simul."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"119848","DOI":"10.1016\/j.ins.2023.119848","article-title":"A consensus model considers managing manipulative and overconfident behaviours in large-scale group decision-making","volume":"654","author":"Liang","year":"2024","journal-title":"Inf. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1219","DOI":"10.1007\/s13042-020-01230-3","article-title":"MAGDM-oriented dual hesitant fuzzy multigranulation probabilistic models based on MULTIMOORA","volume":"12","author":"Zhang","year":"2020","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s00500-020-05144-8","article-title":"Developing the comparison techniques of probabilistic hesitant fuzzy elements in multiple criteria decision making","volume":"25","author":"Farhadinia","year":"2020","journal-title":"Soft Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"119500","DOI":"10.1016\/j.ins.2023.119500","article-title":"Scores of hesitant fuzzy elements revisited: \u201cWas sind und was sollen\u201d","volume":"648","author":"Alcantud","year":"2023","journal-title":"Inf. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.inffus.2018.08.006","article-title":"Score-HeDLiSF: A score function of hesitant fuzzy linguistic term set based on hesitant degrees and linguistic scale functions: An application to unbalanced hesitant fuzzy linguistic MULTIMOORA","volume":"48","author":"Liao","year":"2019","journal-title":"Inf. Fusion"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.ins.2021.07.094","article-title":"A decision-theoretic fuzzy rough set in hesitant fuzzy information systems and its application in multi-attribute decision-making","volume":"579","author":"Jiang","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Zeng, W., Song, G., Yin, Q., and Guo, P. (2019, January 13\u201316). Some new distance measures of hesitant fuzzy sets and its application in group decision making. Proceedings of the 2019 15th International Conference on Computational Intelligence and Security (CIS) 2019, Macao, China.","DOI":"10.1109\/CIS.2019.00033"},{"key":"ref_37","first-page":"2165","article-title":"Three-way group decisions based on multigranulation hesitant fuzzy decision-theoretic rough set over two universes","volume":"38","author":"Ma","year":"2020","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2919","DOI":"10.1108\/K-09-2019-0602","article-title":"Three-way group decisions under hesitant fuzzy linguistic environment for green supplier selection","volume":"49","author":"Ma","year":"2020","journal-title":"Kybernetes"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1903\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T11:18:45Z","timestamp":1762514325000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1903"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,7]]},"references-count":38,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["sym17111903"],"URL":"https:\/\/doi.org\/10.3390\/sym17111903","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,11,7]]}}}